The hidden rules that shape human progress

Samuel Arbesman

About the author

Samuel Arbesman is a senior scholar at the Kauffman Foundation and a fellow at the Institute for Quantitative Social Science at Harvard University. His writing has appeared in The New York Times, The Atlantic, New Scientist and The Boston Globe. He is the author of The Half-Life of Facts: Why Everything Has An Expiration Date, he has a blog at Wired Science called Social Dimension, and you can find him on Twitter at @arbesman.

Our lives are governed by centuries of advances that haven’t been random, as mathematician and network scientist Samuel Arbesman argues there’s a pattern that reveals how our knowledge has changed over time.

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I had my first experience with the internet in the early 1990s. I activated our 300-baud modem, allowed it to begin its R2-D2-like hissing and whistling, and began to telnet. A window on our Macintosh’s screen began filling with text and announced our connection to the computers at the local university. After exploring a series of text menus, I began my first download: a text document containing Plato’s The Republic, via Project Gutenberg. After what felt like a significant fraction of an hour, I was ecstatic. I can distinctly remember jumping up and down, celebrating that I had this entire book on our computer using nothing but phone lines and a lot of atonal beeping.

It took me almost a decade to actually get around to reading The Republic. By the time I did, the notion that I expressed wonder at such a mundane activity as downloading a text document seemed quaint. In 2012, people stream movies onto their computers nightly without praising the modem gods. We have gone from the days of early web pages, with their garish backgrounds and blinking text, to slick interactive sites with enough bells and whistles to make the entire experience smooth and multimedia based. No one thinks any longer about modems or the details of bandwidth speeds. And certainly no one uses the word baud anymore.

The changes haven’t ended there. To store data, I have used floppy disks, diskettes, zip discs, rewritable CDs, flash drives, burnable DVDs, even the Commodore Datasette. Now, I save many of my documents to storage that’s available anytime I have access to the internet: the cloud.

The technological revolution we’re currently experiencing is not a one-off, technology has been changing over the centuries. But what’s surprising is that if you look below the surface you discover that this progress is not random or erratic, it almost always follows a pattern. And understanding this pattern helps us to appreciate far more than faster download speeds or improved data storage. It helps us to understand something fundamental to our success as a species. It helps us to understand how our knowledge changes and evolves.

Double up

In technology, the best-known example of this pattern is Moore’s Law, which states that the processing power of a single chip or circuit will double every year. Gordon Moore, a retired chemist and physicist as well as the co-creator of the Intel Corporation, wasn’t famous or fabulously wealthy when he developed his law. In fact, he hadn’t even founded Intel yet.

In 1965, Moore wrote a short paper, entitled Cramming More Components Onto Integrated Circuits, where he predicted the number of possible components placed on a single circuit for a fixed cost would double every year. He didn’t arrive at this conclusion through exhaustive amounts of data gathering and analysis; in fact, he based his law on only four data points.

The incredible thing is that he was right. This law has held roughly true since 1965; it has weathered the personal computer revolution, the march of processors from 286 to 486 to Pentium, and the many advances since then. While further data has shown that the period for doubling is closer to eighteen months than a year, the principle stands. Processing power grows every year at a constant rate rather than by a constant amount. And according to the original formulation, the annual rate of growth is about 200%.

But when processing power doubles rapidly it allows much more to be possible, and therefore many other developments occur as a result. For example, the number of pixels that digital cameras can process has increased directly due to the regularity of Moore’s Law. This ongoing doubling of technological capabilities has even reached the world of robots. Rodney Brooks, a professor at MIT and a pioneer in the field, found that how far and how fast a robot can move goes through a doubling about every two years: right on schedule and similar to Moore’s Law.

You could argue that this has become a self-fulfilling prophecy. Once Moore’s prediction came to pass, it was simply a matter of working hard to ensure it continued to do so. The industry has a continued stake in trying to reach the next milestone predicted by Moore’s Law, because if any company ever fell behind this curve, it would be out of business.

But while Moore provided a name to something, the phenomenon he named didn’t actually create it. If you generalise Moore’s Law from chips to simply thinking about information technology and processing power in general, Moore’s Law becomes the latest in a long line of technical rules of thumb that explain extremely regular changes in technology over the last few centuries.

Chris Magee, a professor at MIT in the Engineering Systems Division, has measured these changes. Together with his postdoctoral fellow, Heebyung Koh, he compiled a vast data set of all the different instances of information transformation that have occurred throughout history. By lining up one technology after another – from calculations done by hand in 1892 that clocked in at a little under one calculation a minute to today’s machines – a pattern emerged. Despite the differences among all of these technologies, human brains, punch cards, vacuum tubes, integrated circuits, the overall increase in humanity’s ability to perform calculations has progressed quite smoothly and extremely quickly. Put together, there has been a roughly exponential increase in our information transformation abilities over time.

But how does this happen? How can all of these combined technologies yield such a smooth and regular curve? When someone develops a new innovation, it is often largely untested. As its developers improve and refine it, they begin to realise the potential of this new innovation. Its capabilities begin to grow exponentially, but then a limit is reached. And when that limit is reached there is the opportunity to bring in a new technology, even if it’s still tentative, untested and buggy. Combine all these successions of technologies together and what you get is a smooth curve of progresss.

Giant’s shoulders

So technological knowledge exhibits rapid growth just like scientific knowledge. But the relationship between the progression of technological facts and that of science is tightly intertwined.

Take the periodic table of chemical elements. We know that the number of known elements has steadily increased over time. However, while the number appears to have grown relatively smoothly over the centuries, if you look at the data more closely, a different picture emerges. As science historian Derek de Solla Price found, the periodic table has grown by a series of logistic curves. He argued that each of these was due to a successive technological advance or approach. For example, from the beginnings of the scientific revolution in the late 17th Century until the late 19th Century, more than sixty elements were discovered, using various chemical techniques, including electrical shocks, to separate compounds into their constituent parts.

However, these approaches soon reached their limits, and the discoveries slowed. But, following a Moore’s Law-like trajectory, a new technology arose. The particle accelerator was created, and its atom-smashing ability enabled further discoveries. As particle accelerators of increasing energies have been developed, we have discovered heavier and larger chemical elements. In a very real way, these advances have allowed for new facts.

Technological growth facilitates changes in facts, sometimes rapidly, in many areas: sequencing new genomes (nearly two hundred distinct species were sequenced as of late 2011); finding new asteroids (often done using sophisticated computer algorithms that can detect objects moving in space); even proving new mathematical theorems through increasing computer power.

The question is why everything adheres to these exponential curves and grows so rapidly. A likely answer is related to the idea of cumulative knowledge. Anything new – an idea, discovery, or technological breakthrough – must be built upon what is known already. This is generally how the world works. Scientific ideas build upon one another to allow for new scientific knowledge and technologies, and are the basis for new breakthroughs. When it comes to technological and scientific growth, we can bootstrap what we have learned towards the creation of new facts. We must gain a certain amount of knowledge in order to learn something new.

So, while exponential growth is not a self-fulfilling proposition, there is feedback, which leads to a sort of technological imperative: as there is more technological or scientific knowledge on which to grow, new technologies increase the speed at which they grow. But why does this continue to happen? Technological or scientific change doesn’t happen automatically; people are needed to create new ideas and concepts. The answer is that in addition to knowledge accumulation, we need to understand another factor that’s important to knowledge progression: population growth.

Kremer does this in an elegant way, making only a small set of assumptions. First, he states that population growth is limited by technological progress. This is one of those assumptions that has been around since Thomas Malthus, and it is based on the simple fact that as a population grows we need more technology to sustain the population, whether through more efficient food production, more efficient waste management, or other similar considerations. Conversely, Kremer also states that technological growth should be proportional to population size. If invention occurs at the same rate for each person, the more people there are, the more innovation there should be. (More recent research, however, shows that population density often causes innovation to grow faster than population size, so this seems like an underestimate.)

Travel and communication must also play a significant role in the spread of facts and knowledge. For instance, David Bradley, a British epidemiologist, discovered the extent to which populations have spread in an elegant way.

He plotted the lifetime distances travelled by the men in his family over four generations. His great grandfather only travelled around the village of Kettering, north of London – which could be encompassed in a square that is about 25 miles (40 kilometres) on each side. His grandfather, however, travelled as far as London, defined by a square that is about 250 miles (400 km) on each side. Bradley’s father was even more cosmopolitan and travelled throughout Europe; his lifetime movements could be spread throughout a space around 2,500 miles (4,000 km) on each side. Bradley himself, a world-famous scientist, travelled across the globe. While the Earth is not a square grid, he travelled in a range that is around 25,000 miles (40,000 km) on a side, about the circumference of the Earth. A Bradley man moved ten times farther throughout the course of his life with each successive generation, an exponential increase of an order of magnitude more extensive in each direction than his father.

Bradley was concerned with the effect that this increase in travel would have on the spread of disease. But the Bradley family’s exponentially increasing travel distances illustrates not only advances in technology; it is indicative of how technology’s march can itself allow for the greater dispersal of other knowledge.

The speed at which individuals, information and ideas can spread has greatly increased in the past several hundred years. And, unsurprisingly, it has done so according to mathematical rules. The upper limit of travel distances made by people in France in a single day has exponentially increased over a 200-year period, for example, mirroring Bradley’s anecdotal evidence. Similar trends hold for air and sea transportation. The curves for sea transport begin a bit earlier (around 1750), and air transit of course starts later (from the 1920s onwards), but like movement over land, these other modes of transportation obey clear mathematical regularities.

These transportation speeds have clear implications for how the world around us changes. For instance, Cesare Marchetti, an Italian physicist and systems analyst, examined the city of Berlin in great detail and showed that the city has grown in tandem with technological developments. From its early dimensions, when it was hemmed in by the limits of pedestrians and coaches, to later times, when its size ballooned alongside the electric trams and subways, Berlin’s general shape was dictated by the development of ever more powerful technologies.

Marchetti showed that Berlin’s expanse grew according to a simple rule of thumb: the distance reachable by current technologies in thirty minutes or less. As travel speeds increased, so too did the distance traversable and the size of the city.

So we arrive at the foundations of a variety of ever-changing facts based on the development of travel technologies: the natural size of a city; how long information takes to wing its way around the world; and how distant a commute a reasonable person might be expected to endure. And from communication and urban growth to information processing and medical developments, the facts of our everyday lives are governed by technological progress.

While the details of each technological development might be unknown – what I can download, or how many more transistors can be crammed into a square inch, for instance – there are mathematically defined, predictable regularities to how these changes occur. All of these facts, ever changing, are subject to the rules of technological change. And more often than not these ultimately follow a defined pattern: their own mini-Moore’s Law.